Very interesting. I never really gave it much thought. Then again, I don't go to bars and don't get rowdy at public events to have a security guard, bouncer, or off-duty cop have to man-handle me.

Good points, though. Their uniform definitely adds weight to their instructions. I've seen it many times at games and concerts (those are off-duty cops at those events, right?)

Yes they are off-duty. That's why you see uniforms which are way outside their jurisdiction.

As I said to me it is about the dramatically different ramifications for behaving in exactly the same way to two guys who may be in exactly the same place providing security, and then how that potentially affects their behavior.